带有积分边值条件的分数阶微分包含解的存在性  

The Existence of Solutions of Fractional Differential Inclusions with Integral Boundary Value Conditions

作　　者：李建利 陈丽珍[2] 李刚[3] LIJianli;CHEN Lizhen;LI Gang(Department of Applied Mathematics,Taiyuan Institute,Taiyuan,Shanxi,030032,P.R.China;School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan,Shanxi,030006,P.R.China;School of Mathematical Sciences,Yangzhou University,Yangzhou,Jiangsu,225002,P.R.China)

机构地区：[1]太原学院应用数学系,山西太原030032 [2]山西财经大学应用数学学院,山西太原030006 [3]扬州大学数学科学学院,江苏扬州225002

出　　处：《数学进展》2020年第2期185-194,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11871064)。

摘　　要：本文利用Hausdorff非紧测度、分数阶的微积分理论和Kakutani不动点定理,研究了满足条件z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds的广义Bagley-Torvik型分数阶微分包含cDv1 z(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)解的存在性.其中1 <v1 <2,1≤v2<v1,0<η<1,γ=v1-v2>0,a和λ是给定的常数.We consider the generalized Bagley-Torvik type fractional differential inclusion cDv1(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)meet to z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds,where 1 <v1<2,1≤v2<v1,0 <η≤1,γ=v1-v2>0,a and λ are given constants in this article.By the noncompactness measure of Hausdorff,fractional calculus theory and Kakutani fixed point theorem,we prove the existence of solutions.Our result extends the existence theorems for the Bagley-Torvik type equation.

关 键 词：HAUSDORFF非紧测度 分数阶微分包含 KAKUTANI不动点定理 

分 类 号：O175.8[理学—数学]